Simplify Square Root of 4853

What is the square root of 4853 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√4853 = A√B

Unfortunately, the square root of 4853 cannot be simplified. Thus, here is the answer to the square root of 4853 in its simplest form:

√ 4853 = √ 4853

Here are two different methods we used to determine why the square root of 4853 cannot be simplified.

1) To be able to simplify the square root of 4853, one of the factors of 4853 other than 1 must be a perfect square. The factors of 4853 are 1, 23, 211, and 4853. Since none of these factors are perfect squares, the square root of 4853 cannot be simplified.

2) To be able to simplify the square root of 4853, all the prime factors of 4853 cannot be unique. When we did prime factorization of 4853, we found that 23 x 211 equals 4853. Since all the prime factors are unique, the square root of 4853 cannot be simplified.

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